Critical sets for a pair of mutually orthogonal cyclic latin squares of odd order greater than 9

R. SahaRay, Indian Statistical Institute, India
A. Adhikari, Indian Statistical Institute, India
J. Seberry, University of Wollongong

Article comments

This article was originally published as SahaRay, R, Adhikari, A and Seberry, J, Critical sets for a pair of mutually orthogonal cyclic latin squares of odd order greater than 9, Journal of Combinatorial Mathematics and Combinatorial Computing, 55, 2005, 171-185.

Abstract

To date investigations on critical sets for a set of mutually orthogonal latin squares (MOLS) have been carried out only for small orders less than or equal to 9. In this paper we deal with a pair of cyclic orthogonal latin squares of order n, n greater than or equal to 11, n odd. Through construction of a uniquely completable set we give an upper bound on the size of the minimal critical set. In particular for n = 15 a critical set achieving this bound is obtained.